Note that SKL manifolds includes all Strominger flat manifolds, which were classified by Q. Wang, B. Yang and the second named author in [1]} as quotients of Samelson spaces, namely, Lie-Hermitian manifolds with bi-invariant metrics. More precisely, by Milnor's Lemma [2]}, the universal cover is the product of a compact semi-simple Lie group with a vector group, equipped with a bi-invariant metric and a compatible left invariant complex structure.
